20210207, 15:28  #12  
"Alexander"
Nov 2008
The Alamo City
577 Posts 
Quote:
I also ran a third or so of a t30 (ECM) on the cofactor of that number (which is nowhere near small for factorization, where 200 digits is huge for nonspecial forms), with no dice. 

20210207, 15:55  #13 
Jan 2017
2^{2}·7 Posts 
Other closed form of the Hugo sequence and observations
There is a much simpler closed form for the Hugo Numbers than what has been posted by Hugo and the others, they are equal to:
(Sum from k=0 to k=(p1)/2 of (Binomial(p, 2*k)*13^k))/2^(n1) It can also be shown that the Hugo Numbers are, in the limit, a geometric series, with first term 1/2(1+sqrt(13)) and common ratio 1/2(7+sqrt(13)). There are also Mersennelike primality characteristics of this sequence that I have observed (Hugo(y*x) = Hugo(y) * Hugo(x) * cofactor unless y*x is a perfect power, divisors of Hugo(n) with N prime of specific forms either 2*k*p+1 or 2*k*p1) 
20210207, 20:54  #14  
Dec 2008
you know...around...
3^{2}·71 Posts 
Quote:
2^82589933+80875047 2^82589933+148316925 2^82589933+205790751 2^82589933+326805255 2^82589933+382879239 2^82589933+432870647 2^82589933+516518021 2^82589933+768187217 2^82589933+785549457 2^82589933+861000575 2^82589933+919430651 2^82589933+937150935 2^82589933+966499157 2^82589933+974862225 2^82589933+981502331 2^82589933+984925185 2^82589933+1016742659 2^82589933+1114725015 2^82589933+1189890905 2^82589933+1315732101 2^82589933+1337194461 2^82589933+1386199751 2^82589933+1402635029 2^82589933+1602826059 2^82589933+1628081609 2^82589933+1674437519 2^82589933+1711934037 2^82589933+1724772015 2^82589933+1988025401 2^82589933+2081143619 2^82589933+2101268115 2^82589933+2161866755 2^82589933+2182473311 2^82589933+2223069261 2^82589933+2248242831 Sorry, I really couldn't resist. It was an unfinished project in my drawer. Please don't waste any of your precious time. 

20210207, 21:21  #15  
"Kebbaj Reda"
May 2018
Casablanca, Morocco
83 Posts 
Quote:
Hugo compare his numbers with Mersenne primes which are very large, if you wanted to have fun proving a number of 1 million digits with ECPP, have fun alone. Last fiddled with by Kebbaj on 20210207 at 21:46 

20210207, 22:21  #16 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2^{3}×3^{2}×5×17 Posts 
Go ahead and prove those are prime. We'll wait.
Last fiddled with by retina on 20210207 at 22:22 
20210208, 04:33  #17 
"Alexander"
Nov 2008
The Alamo City
241_{16} Posts 
Sorry, I had a migraine last night and got my wires crossed with the number in that post, which I was trying to factor p1 for (which is clearly not top 5k). Yeah, no chance to prove a 1M+ digit number with ECPP.

20210208, 18:03  #18 
Dec 2008
you know...around...
639_{10} Posts 

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